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Peer reviewed
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Saha, Laxman; Basunia, Alamgir R.; Das, Satyabrata; Tiwary, Kalishankar
Theory of computing systems, 02/2022, Volume: 66, Issue: 1Journal Article
For a simple connected graph G = ( V ( G ), E ( G )) and a positive integer k , a radio k -labelling of G is a mapping f : V ( G ) → { 0 , 1 , 2 , … } such that | f ( u ) − f ( v ) | ≥ k + 1 − d ( u , v ) for each pair of distinct vertices u and v of G , where d ( u , v ) is the distance between u and v in G . The radio k-chromatic number is the minimum span of a radio k -labeling of G . In this article, we study the radio k -labelling problem for complete m -ary trees T m , h and determine the exact value of radio k -chromatic number for these trees when k ≥ 2 h − 1.
